Free access
Issue
ESAIM: COCV
Volume 12, Number 1, January 2006
Page(s) 93 - 119
DOI http://dx.doi.org/10.1051/cocv:2005029
Published online 15 December 2005
  1. F. Abergel and R. Temam, On some control problems in fluid mechanics. Theoret. Comput. Fluid Dynam. 1 (1990) 303–325. [CrossRef]
  2. R.A. Adams, Sobolev spaces. Academic Press, San Diego (1978).
  3. N. Arada, J.-P. Raymond and F. Tröltzsch, On an augmented Lagrangian SQP method for a class of optimal control problems in Banach spaces. Comput. Optim. Appl. 22 (2002) 369–398. [CrossRef] [MathSciNet]
  4. J.F. Bonnans, Second-order analysis for control constrained optimal control problems of semilinear elliptic equations. Appl. Math. Optim. 38 (1998) 303–325. [CrossRef] [MathSciNet]
  5. J.F. Bonnans and H. Zidani, Optimal control problems with partially polyhedric constraints. SIAM J. Control Optim. 37 (1999) 1726–1741. [CrossRef] [MathSciNet]
  6. H. Brezis, Analyse fonctionelle. Masson, Paris (1983).
  7. E. Casas, An optimal control problem governed by the evolution Navier-Stokes equations, in Optimal control of viscous flows. Frontiers in applied mathematics, S.S. Sritharan Ed., SIAM, Philadelphia (1993).
  8. E. Casas and M. Mateos, Second order optimality conditions for semilinear elliptic control problems with finitely many state constraints. SIAM J. Control Optim. 40 (2002) 1431–1454. [CrossRef] [MathSciNet]
  9. E. Casas and M. Mateos, Uniform convergence of the FEM. Applications to state constrained control problems. Comp. Appl. Math. 21 (2002) 67–100.
  10. E. Casas, F. Tröltzsch and A. Unger, Second-order sufficient optimality conditions for a nonlinear elliptic control problem. J. Anal. Appl. 15 (1996) 687–707.
  11. E. Casas, F. Tröltzsch and A. Unger, Second-order sufficient optimality conditions for some state-constrained control problems of semilinear elliptic equations. SIAM J. Control Optim. 38 (2000) 1369–1391. [CrossRef] [MathSciNet]
  12. P. Constantin and C. Foias, Navier-Stokes equations. The University of Chicago Press, Chicago (1988).
  13. R. Dautray and J.L. Lions, Evolution problems I, Mathematical analysis and numerical methods for science and technology 5. Springer, Berlin (1992).
  14. M. Desai and K. Ito, Optimal controls of Navier-Stokes equations. SIAM J. Control Optim. 32 (1994) 1428–1446. [CrossRef] [MathSciNet]
  15. A.L. Dontchev, W.W. Hager, A.B. Poore and B. Yang, Optimality, stability, and convergence in optimal control. Appl. Math. Optim. 31 (1995) 297–326. [CrossRef] [MathSciNet]
  16. J.C. Dunn, On second-order sufficient conditions for structured nonlinear programs in infinite-dimensional function spaces, in Mathematical programming with data perturbations, A. Fiacco Ed., Marcel Dekker (1998) 83–107.
  17. H.O. Fattorini and S. Sritharan, Necessary and sufficient for optimal controls in viscous flow problems. Proc. Roy. Soc. Edinburgh 124 (1994) 211–251.
  18. M.D. Gunzburger Ed., Flow control. Springer, New York (1995).
  19. M.D. Gunzburger and S. Manservisi, The velocity tracking problem for Navier-Stokes flows with bounded distributed controls. SIAM J. Control Optim. 37 (1999) 1913–1945. [CrossRef] [MathSciNet]
  20. M.D. Gunzburger and S. Manservisi, Analysis and approximation of the velocity tracking problem for Navier-Stokes flows with distributed control. SIAM J. Numer. Anal. 37 (2000) 1481–1512. [CrossRef] [MathSciNet]
  21. M. Hinze, Optimal and instantaneous control of the instationary Navier-Stokes equations. Habilitation, TU Berlin (2002).
  22. M. Hinze and K. Kunisch, Second-order methods for optimal control of time-dependent fluid flow. SIAM J. Control Optim. 40 (2001) 925–946. [CrossRef] [MathSciNet]
  23. H. Maurer and J. Zowe, First- and second-order conditions in infinite-dimensional programming problems. Math. Programming 16 (1979) 98–110. [CrossRef] [MathSciNet]
  24. H.D. Mittelmann and F. Tröltzsch, Sufficient optimality in a parabolic control problem, in Trends in Industrial and Applied Mathematics, A.H. Siddiqi and M. Kocvara Ed., Dordrecht, Kluwer (2002) 305–316.
  25. J.-P. Raymond and F. Tröltzsch, Second order sufficient optimality conditions for nonlinear parabolic control problems with state constraints. Discrete Contin. Dynam. Syst. 6 (2000) 431–450. [CrossRef] [MathSciNet]
  26. T. Roubíček and F. Tröltzsch, Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations. Control Cybernet. 32 (2002) 683–705.
  27. S. Sritharan, Dynamic programming of the Navier-Stokes equations. Syst. Control Lett. 16 (1991) 299–307. [CrossRef]
  28. R. Temam, Navier-Stokes equations. North Holland, Amsterdam (1979).
  29. F. Tröltzsch, Lipschitz stability of solutions of linear-quadratic parabolic control problems with respect to perturbations. Dyn. Contin. Discrete Impulsive Syst. 7 (2000) 289–306.